---
name: "dtrsyl"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dtrsyl/3lapack"
---

# dtrsyl(3lapack)

solves the real Sylvester matrix equation

## NAME

DTRSYL - solves the real Sylvester matrix equation

## SYNOPSIS

- SUBROUTINE DTRSYL(

  TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, LDC, SCALE, INFO )

- CHARACTER

  TRANA, TRANB

- INTEGER

  INFO, ISGN, LDA, LDB, LDC, M, N

- DOUBLE

  PRECISION SCALE

- DOUBLE

  PRECISION A( LDA, \* ), B( LDB, \* ), C( LDC, \* )

## PURPOSE

DTRSYL solves the real Sylvester matrix equation:\
    op(A)\*X + X\*op(B) = scale\*C or\
\
    op(A)\*X - X\*op(B) = scale\*C,\
 where op(A) = A or A\*\*T, and  A and B are both upper quasi- triangular. A is M-by-M and B is N-by-N; the right hand side C and the solution X are M-by-N; and scale is an output scale factor, set \<= 1 to avoid overflow in X.\
 A and B must be in Schur canonical form (as returned by DHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign.\

## ARGUMENTS

- TRANA (input) CHARACTER\*1

  Specifies the option op(A):\
   \= 'N': op(A) = A    (No transpose)\
   \= 'T': op(A) = A\*\*T (Transpose)\
   \= 'C': op(A) = A\*\*H (Conjugate transpose = Transpose)

- TRANB (input) CHARACTER\*1

  Specifies the option op(B):\
   \= 'N': op(B) = B    (No transpose)\
   \= 'T': op(B) = B\*\*T (Transpose)\
   \= 'C': op(B) = B\*\*H (Conjugate transpose = Transpose)

- ISGN (input) INTEGER

  Specifies the sign in the equation:\
   \= +1: solve op(A)\*X + X\*op(B) = scale\*C\
   \= -1: solve op(A)\*X - X\*op(B) = scale\*C

- M (input) INTEGER

  The order of the matrix A, and the number of rows in the matrices X and C. M \>= 0.

- N (input) INTEGER

  The order of the matrix B, and the number of columns in the matrices X and C. N \>= 0.

- A (input) DOUBLE PRECISION array, dimension (LDA,M)

  The upper quasi-triangular matrix A, in Schur canonical form.

- LDA (input) INTEGER

  The leading dimension of the array A. LDA \>= max(1,M).

- B (input) DOUBLE PRECISION array, dimension (LDB,N)

  The upper quasi-triangular matrix B, in Schur canonical form.

- LDB (input) INTEGER

  The leading dimension of the array B. LDB \>= max(1,N).

- C (input/output) DOUBLE PRECISION array, dimension (LDC,N)

  On entry, the M-by-N right hand side matrix C. On exit, C is overwritten by the solution matrix X.

- LDC (input) INTEGER

  The leading dimension of the array C. LDC \>= max(1,M)

- SCALE (output) DOUBLE PRECISION

  The scale factor, scale, set \<= 1 to avoid overflow in X.

- INFO (output) INTEGER

  \= 0: successful exit\
   \< 0: if INFO = -i, the i-th argument had an illegal value\
   \= 1: A and B have common or very close eigenvalues; perturbed values were used to solve the equation (but the matrices A and B are unchanged).